1. Solve the following equations:

(a) 2y + \frac{5}{2} = \frac{37}{2}

 (b) 5t + 28 = 10

(c) a /5 + 3 = 2

(d) q/ 4 + 7 = 5

 e) 5 x/2  = –5

(f) \frac{5}{2}x = \frac{25}{4}

(g) 7m + 19/2 = 13 

(h) 6z + 10 = –2

(i)\frac{3l}{2} = 2/3

(j)\frac{2b}{3}- 5 = 3

Answers (1)

(a) 2y + \frac{5}{2} = \frac{37}{2}

    Transposing \frac{5}{2} to the RHS :

 2y\ =\ \frac{37}{2}\ -\ \frac{5}{2}\ =\ 16

 y\ =\ 8

 

(b)    5t + 28 = 10

Transposing 28 to the RHS and then dividing both sides by 5, we get  :

  5t\ =\ 10\ -\ 28\ =\ -\ 18

  t\ =\ -\frac{18}{5}

 

(c)  a /5 + 3 = 2

Transposing 3 to the RHS and multiplying both sides by 5, we get :

   \frac{a}{5}\ +\ 3\ =\ 2

  \frac{a}{5}\ =\ -\ 1

   a\ =\ -\ 5

 

(d)  q/ 4 + 7 = 5

Transposing 7 to the RHS and multiplying both sides by 4:

    \frac{q}{4}\ +\ 7\ =\ 5

     \frac{q}{4}\ =\ -\ 2

  q\ =\ -\ 8

 

(e)     5 x/2  = – 5

Multiplying both sides by \frac{2}{5} :

  x\ =\ -5\times \frac{2}{5}\ =\ -\ 2

 

(f)   \frac{5}{2}x = \frac{25}{4}

Multiplying both sides by \frac{2}{5} :

   x\ =\ \frac{25}{4}\times \frac{2}{5}

  x\ =\ \frac{5}{2}

 

(g)   7m + 19/2 = 13

Transposing \frac{19}{2}  to the RHS and then dividing both sides by 7 :

 7m\ =\ 13\ -\ \frac{19}{2}\ =\ \frac{7}{2}

   m\ =\ \frac{1}{2}

 

(h)  6z + 10 = –2

Transposing 10 to the RHS and then dividing both sides by 6, we get :

  6z\ =\ -\ 2\ -\ 10\ =\ -\ 12

  z\ =\ -\ 2

 

(i)      \frac{3l}{2} = 2/3

Multiplying both sides by  \frac{2}{3},

  l\ =\ \frac{2}{3}\times \frac{2}{3}\ =\ \frac{4}{9}

 

(j)     \frac{2b}{3}- 5 = 3

Transposing 5 to the RHS and then multiplying both sides by \frac{3}{2}

  \frac{2b}{3}\ =\ 8

 b\ =\ 8\times \frac{3}{2}\ =\ 12

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